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Simplifying (-9 + 2i) + -1(-12 + 4i) = 0 Remove parenthesis around (-9 + 2i) -9 + 2i + -1(-12 + 4i) = 0 -9 + 2i + (-12 * -1 + 4i * -1) = 0 -9 + 2i + (12 + -4i) = 0 Reorder the terms: -9 + 12 + 2i + -4i = 0 Combine like terms: -9 + 12 = 3 3 + 2i + -4i = 0 Combine like terms: 2i + -4i = -2i 3 + -2i = 0 Solving 3 + -2i = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -2i = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2i = 0 + -3 -2i = 0 + -3 Combine like terms: 0 + -3 = -3 -2i = -3 Divide each side by '-2'. i = 1.5 Simplifying i = 1.5
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